Rival approaches to mathematical modelling in immunology

In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.     

Molding loose metal particles into briquettes with the use of short pulses of high density current

Theoretical estimates and experimental investigations were carried out on the process of molding a mixture of metal particles and a dielectric (air) into briquettes with the use of short pulses of high density current. Four groups of specimens were studied consisting of metal fragments and the dielectric in various proportions. In the experiments and the current and voltage oscillograms, the electrical resistance and the temperature of the specimens before and after passing the current were measured and their ultimate strength was determined. It has been found that the processes affecting the distribution of the current over the specimen cross section and the specimen inductance during the current pulse play an important role in molding briquettes of sufficient strength for transportation and processing.     

Quantum chemical simulations of titanium dioxide nanotubes used for photocatalytic water splitting

Titanium dioxide nanotubes (NTs) built from various initial 2D models of TiO2 (a promising catalyst for water splitting) are investigated via density functional theory using the B3LYP hybrid exchange-correlation functional in the localized basis set of a linear combination of atomic orbitals. For TiO₂ NTs (eight different types of morphology) created from four initial 2D structures, full geometry optimization is performed and the main energy parameters, such as the band gap width, energy positions of the valence band top and the conduction band bottom, and NT formation and strain energy, are calculated. Analysis of the NT strain and formation energies enables us to choose their most stable configuration, which can further be employed to simulate NTs doped with impurity atoms capable of serving as efficient centers for the photocatalytic dissociation of water molecules.     

Reduction of threshold of acousto-optic effect in a nematic crystal subject to combined actions

The acousto-optic effect in a homeotropically aligned layer of a nematic liquid crystal was investigated subject to combined actions: 1, for coherent excitation of ultrasonic and viscous waves, 2, for ultrasonic action in an electric field near the Freedericksz transition. The acousto-optic effect threshold was reduced by two orders of magnitude. The experimental results are discussed using the facoustic streaming model. The theoretical analysis is supported by our experimental results.     

Percolation Transition Under Thermal Reduction of Graphene Oxide

The conductivity of thermally reduced graphene oxide (GO) measured at various reduction stages shows that the samples demonstrate transition to the conducting state within a narrow range of annealing temperatures (150-170 °С). The conductivity in this temperature region increases by about five orders of magnitude to indicate that the percolation mechanism is responsible for this transition. According to this mechanism, the above temperature range is associated with formation of a certain number of conductive channels composed of GO fragments reduced to the conducting state. Thus, it is a new type of percolation transition, since increased conductivity is a result of increased conductivity of the particles due to thermal treatment rather than a result of increased concentration of conducting particles. A further temperature growth is associated with increased number of conducting GO fragments and the number of conducting channels, and some smoother conductivity increase. The XPS spectra of partially reduced GO samples indicate correlation between increased conductivity of GO fragments and plasmon oscillations revealed as XPS peaks. The current-voltage characteristics measured for the samples of partially reduced GO indicate a non-ohmic conductivity which manifests as increased conductivity versus voltage dependence. This is due to the fact that electrical resistance of the percolation channels is the sum of resistances of conductive GO fragments and contact resistances which depend on the voltage drop at the contact and, therefore, on the voltage applied.     

Vibrational spectrum of perfluoroethane

We have obtained IR absorption spectra of a C₂F₆ gas and a C₂F₆ cryosolution in Xe (T = 163 K) in the fundamental and overtone ranges. We have interpreted 28 bands of ¹²C¹²CF₆ and three bands of ¹³C¹²CF₆. In the spectral ranges that correspond to vibrations that are combinations with ν₁, ν₇, and ν₅, we observe multiplets, which we attribute to interactions of the type of Fermi resonances between the states ν₁(A _1g ) ∼ ν₆(A _1g ), ν₇(E _g ) ∼ ν₆ + ν₁₁(E _g ) ∼ 2ν₈(E _g ), ν₅(A _2u ) ∼ ν₈ + ν ₁₁(A _2u ). We reveal an anomalous intensity distribution in the spectrum of an asymmetric isotopologue. For the basic and isotopic configurations of perfluoroethane, we calculate the coefficients of shapes of vibrations and the intensities of absorption bands. We reveal that the behavior of the groups ¹²CF₃ and ¹³CF₃ is indifferent to the excitation of doubly degenerate stretching vibrations ν₇(E _g ) and ν₁₀(Eu).